Problem of the Week

Updated at Aug 23, 2021 5:59 PM

To get more practice in equation, we brought you this problem of the week:

How would you solve \(\frac{{x}^{2}}{5}(5-\frac{5}{x})=6\)?

Check out the solution below!



\[\frac{{x}^{2}}{5}(5-\frac{5}{x})=6\]

1
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[\frac{{x}^{2}(5-\frac{5}{x})}{5}=6\]

2
Factor out the common term \(5\).
\[\frac{{x}^{2}\times 5(1-\frac{1}{x})}{5}=6\]

3
Regroup terms.
\[\frac{5{x}^{2}(1-\frac{1}{x})}{5}=6\]

4
Cancel \(5\).
\[{x}^{2}(1-\frac{1}{x})=6\]

5
Expand.
\[{x}^{2}-x=6\]

6
Move all terms to one side.
\[{x}^{2}-x-6=0\]

7
Factor \({x}^{2}-x-6\).
\[(x-3)(x+2)=0\]

8
Solve for \(x\).
\[x=3,-2\]

Done
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